Cardinal numbers proof (identities) & Classes/Sets

Hi, I need to prove the following rules on cardinal numbers:

Question1) For all cardinal numbers, κ:

1) κ + 0 = κ,

2) κ·0 = 0,

3) κ·1 = κ.

Note: = is in terms of equal cardinality.

This looks obvious, but I just dont know how to write it in a nice formal way.

My other question is about Classes / Sets

Question2) For any two disjoint sets A, B, the class

Σ(A,B) = {W | W is a connection of A with B}

is a set.

How can I show this in a nice clean way?

Help would be nice!

Thanks! (Nod)